89 ideas
| 12926 | Wisdom is the science of happiness [Leibniz] |
| 12903 | Wise people have fewer acts of will, because such acts are linked together [Leibniz] |
| 12914 | Metaphysics is geometrical, resting on non-contradiction and sufficient reason [Leibniz] |
| 12915 | Definitions can only be real if the item is possible [Leibniz] |
| 12910 | The predicate is in the subject of a true proposition [Leibniz] |
| 19333 | A truth is just a proposition in which the predicate is contained within the subject [Leibniz] |
| 13689 | 'Theorems' are formulas provable from no premises at all [Sider] |
| 13705 | Truth tables assume truth functionality, and are just pictures of truth functions [Sider] |
| 13706 | Intuitively, deontic accessibility seems not to be reflexive, but to be serial [Sider] |
| 13710 | In D we add that 'what is necessary is possible'; then tautologies are possible, and contradictions not necessary [Sider] |
| 13711 | System B introduces iterated modalities [Sider] |
| 13708 | S5 is the strongest system, since it has the most valid formulas, because it is easy to be S5-valid [Sider] |
| 13712 | Epistemic accessibility is reflexive, and allows positive and negative introspection (KK and K¬K) [Sider] |
| 13714 | We can treat modal worlds as different times [Sider] |
| 13720 | Converse Barcan Formula: □∀αφ→∀α□φ [Sider] |
| 13718 | The Barcan Formula ∀x□Fx→□∀xFx may be a defect in modal logic [Sider] |
| 13723 | System B is needed to prove the Barcan Formula [Sider] |
| 13715 | You can employ intuitionist logic without intuitionism about mathematics [Sider] |
| 13678 | The most popular account of logical consequence is the semantic or model-theoretic one [Sider] |
| 13679 | Maybe logical consequence is more a matter of provability than of truth-preservation [Sider] |
| 13682 | Maybe logical consequence is impossibility of the premises being true and the consequent false [Sider] |
| 13680 | Maybe logical consequence is a primitive notion [Sider] |
| 13722 | A 'theorem' is an axiom, or the last line of a legitimate proof [Sider] |
| 13696 | When a variable is 'free' of the quantifier, the result seems incapable of truth or falsity [Sider] |
| 13700 | A 'total' function must always produce an output for a given domain [Sider] |
| 13703 | λ can treat 'is cold and hungry' as a single predicate [Sider] |
| 13688 | Good axioms should be indisputable logical truths [Sider] |
| 13687 | No assumptions in axiomatic proofs, so no conditional proof or reductio [Sider] |
| 13690 | Proof by induction 'on the length of the formula' deconstructs a formula into its accepted atoms [Sider] |
| 13691 | Induction has a 'base case', then an 'inductive hypothesis', and then the 'inductive step' [Sider] |
| 13685 | Natural deduction helpfully allows reasoning with assumptions [Sider] |
| 13686 | We can build proofs just from conclusions, rather than from plain formulae [Sider] |
| 13697 | Valuations in PC assign truth values to formulas relative to variable assignments [Sider] |
| 13684 | The semantical notion of a logical truth is validity, being true in all interpretations [Sider] |
| 13704 | It is hard to say which are the logical truths in modal logic, especially for iterated modal operators [Sider] |
| 13724 | In model theory, first define truth, then validity as truth in all models, and consequence as truth-preservation [Sider] |
| 13698 | In a complete logic you can avoid axiomatic proofs, by using models to show consequences [Sider] |
| 13699 | Compactness surprisingly says that no contradictions can emerge when the set goes infinite [Sider] |
| 12920 | There is no multiplicity without true units [Leibniz] |
| 13701 | A single second-order sentence validates all of arithmetic - but this can't be proved axiomatically [Sider] |
| 12319 | What is not truly one being is not truly a being either [Leibniz] |
| 12922 | A thing 'expresses' another if they have a constant and fixed relationship [Leibniz] |
| 13692 | A 'precisification' of a trivalent interpretation reduces it to a bivalent interpretation [Sider] |
| 13695 | Supervaluational logic is classical, except when it adds the 'Definitely' operator [Sider] |
| 13693 | A 'supervaluation' assigns further Ts and Fs, if they have been assigned in every precisification [Sider] |
| 13694 | We can 'sharpen' vague terms, and then define truth as true-on-all-sharpenings [Sider] |
| 13683 | A relation is a feature of multiple objects taken together [Sider] |
| 13079 | A substance contains the laws of its operations, and its actions come from its own depth [Leibniz] |
| 12745 | Philosophy needs the precision of the unity given by substances [Leibniz] |
| 12921 | Accidental unity has degrees, from a mob to a society to a machine or organism [Leibniz] |
| 12746 | We find unity in reason, and unity in perception, but these are not true unity [Leibniz] |
| 12916 | A body is a unified aggregate, unless it has an indivisible substance [Leibniz] |
| 12919 | Unity needs an indestructible substance, to contain everything which will happen to it [Leibniz] |
| 12923 | Every bodily substance must have a soul, or something analogous to a soul [Leibniz] |
| 12704 | Aggregates don’t reduce to points, or atoms, or illusion, so must reduce to substance [Leibniz] |
| 13077 | Basic predicates give the complete concept, which then predicts all of the actions [Leibniz] |
| 12908 | Essences exist in the divine understanding [Leibniz] |
| 12706 | Bodies need a soul (or something like it) to avoid being mere phenomena [Leibniz] |
| 12906 | Truths about species are eternal or necessary, but individual truths concern what exists [Leibniz] |
| 13702 | The identity of indiscernibles is necessarily true, if being a member of some set counts as a property [Sider] |
| 13721 | 'Strong' necessity in all possible worlds; 'weak' necessity in the worlds where the relevant objects exist [Sider] |
| 13707 | Maybe metaphysical accessibility is intransitive, if a world in which I am a frog is impossible [Sider] |
| 13709 | Logical truths must be necessary if anything is [Sider] |
| 13716 | 'If B hadn't shot L someone else would have' if false; 'If B didn't shoot L, someone else did' is true [Sider] |
| 12904 | If varieties of myself can be conceived of as distinct from me, then they are not me [Leibniz] |
| 11981 | If someone's life went differently, then that would be another individual [Leibniz] |
| 13717 | Transworld identity is not a problem in de dicto sentences, which needn't identify an individual [Sider] |
| 13719 | Barcan Formula problem: there might have been a ghost, despite nothing existing which could be a ghost [Sider] |
| 12905 | I cannot think my non-existence, nor exist without being myself [Leibniz] |
| 19334 | I can't just know myself to be a substance; I must distinguish myself from others, which is hard [Leibniz] |
| 5033 | Nothing should be taken as certain without foundations [Leibniz] |
| 7458 | The reliability of witnesses depends on whether they benefit from their observations [Laplace, by Hacking] |
| 12913 | Nature is explained by mathematics and mechanism, but the laws rest on metaphysics [Leibniz] |
| 13089 | To fully conceive the subject is to explain the resulting predicates and events [Leibniz] |
| 5034 | Mind is a thinking substance which can know God and eternal truths [Leibniz] |
| 5032 | It seems probable that animals have souls, but not consciousness [Leibniz] |
| 3441 | If a supreme intellect knew all atoms and movements, it could know all of the past and the future [Laplace] |
| 5031 | Everything which happens is not necessary, but is certain after God chooses this universe [Leibniz] |
| 12911 | Concepts are what unite a proposition [Leibniz] |
| 12925 | Beauty increases with familiarity [Leibniz] |
| 12927 | Happiness is advancement towards perfection [Leibniz] |
| 15955 | I think the corpuscular theory, rather than forms or qualities, best explains particular phenomena [Leibniz] |
| 12907 | Each possible world contains its own laws, reflected in the possible individuals of that world [Leibniz] |
| 12924 | Motion alone is relative, but force is real, and establishes its subject [Leibniz] |
| 12909 | Everything, even miracles, belongs to order [Leibniz] |
| 5030 | Miracles are extraordinary operations by God, but are nevertheless part of his design [Leibniz] |
| 12912 | Immortality without memory is useless [Leibniz] |
| 12917 | The soul is indestructible and always self-aware [Leibniz] |
| 12918 | Animals have souls, but lack consciousness [Leibniz] |